The invention is based on a radial piston pump as as set from therein of the kind already known from German Patent Disclosure DE-A1 37 01 857. In that reference, a ring device is provided as the actuating element; on one side of its axial length it is supported on a ball bearing, which in turn is fixed on an eccentric element on the free end of a drive shaft. The known ring device fits over a stublike housing part into which the pump cylinders are radially machined, with pump pistons emerging radially outward from them and there coming to rest on the ring device via cuplike formations. When the eccentric element is driven, the ring device executes a tumbling eccentric motion, in the course of which the pump pistons are moved alternately inward or outward and in so doing execute their intake and supply strokes. In this embodiment of a radial piston pump, although compared with known versions in which the pump pistons slide via centrally located cam races the transferring motions between the actuating element and the pump piston are relatively slight, nevertheless they are still not entirely prevented in the known embodiment. In particular, depending on the rotary position of the ring device, the pump pistons each assume positions in which they are not at right angles to the inside surface of the driving ring device. As a result, there are still shear forces at the point of contact of the pump pistons with the ring device and sliding friction, since because of the construction the surface of the ring device shifts relative to the pump pistons. The known radial piston pump is contemplated in particular for supplying a hydraulic anti-lock brake system; as the medium to be pumped, pressure fluid can be chosen, which within limits has more lubricant properties. However, if such a pump is to be used to generate pressure in media which have from only slight to no lubricating properties, such as gasoline, then high sliding friction must be expected in the contact regions between the pump pistons, leading on the one hand to increased power loss when the radial piston pump is driven and on the other to increased wear. Because of abrasion of material and scuffing with a strong draft on the driving side of the pump pistons, a considerably limited service life must be expected. Pumps that are exposed to gasoline in this region behave as if they were run dry when lubricated.